In a bowl, beat egg; Add sugar and butter. Combine flour, baking powder, cinnamon, nutmeg and salt; and add to sugar mixture alternately with milk. Stir in cranberries. Heat oil in an electric skillet to 375 degrees. Drop by tablespoonsfuls of batter into oil. Fry doughnuts a few at a time, turning with a slotted spoon until golden, About 2 minutes per side. Drain on paper towels; roll in sugar while warm.